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Use the Remainder Theorem to find the remainder when P(x)=x4−9x3−5x2−3x+4
is divided by x+3
.
To find the remainder when P(x) is divided by x+3, we first need to set x+3 equal to 0 and solve for x to find the root of the divisor:
x + 3 = 0
x = -3
Now, we use synthetic division to divide P(x) by x+3:
-3 | 1 -9 -5 -3 4
-3 36 -3
___________________
1 -12 31 1
Therefore, the remainder when P(x) is divided by x+3 is 1.